Table Of ContentContemporary
Research Topics in
NUCLEAR
PHYSICS
Contemporary
Research Topics in
NUCLEAR
PHYSICS
Edited by
Da Hsuan Feng and Michel Vallieres
Drexel University
PhIladelphia, Pennsylvania
and
Michael W. Guidry and Lee L. Riedinger
University of Tennessee
Knoxville, Tennessee
PLENUM PRESS • NEW YORK AND LONDON
Library of Congress Cataloging in Publication Data
Main entry under title:
Contemporary research topics in nuclear physics.
"Proceedings of a workshop held at Drexel University from September 1 to Sep
tember 3, 1980, under the joint auspices of Drexel Umversity, the University of Ten
nessee, and Vanderbilt University" -Pref.
Bibliography: p.
Includes index.
1. Nuclear physics-Congresses. I. Feng, Da Hsuan, 1945- II. Drexel Uni-
versity. III. University of Tennessee (Knoxville campus). IV. Vanderbilt University.
QC770.CC6 539.7 82-3677
ISBN-13:978-1-4684-1136-2 e-ISBN-13:978-1-4684-1134-8
DOl: 10.1007/978-1-4684-1134-8
Proceedings of a workshop on Nuclear Physics, held September
1-3, 1980, at Drexel University, Philadelphia, Pennsylvania
© 1982 Plenum Press, New York
Softcover reprint of the hardcover 1s t edition 1982
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All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted
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PREFACE
This volume contains the proceedings of a workshop held at
Drexel University from September 1 to September 3, 1980, under the
joint auspices of Drexel University, The University of Tennessee
and Vanderbilt University.
The workshop dealt with subjects of topical importance to the
nuclear physics community: high spin phenomena, heavy ion reactions,
transfer reactions, microscopic theories of nuclear structure and
the interacting boson model, and miscellaneous topics. This pro
ceedings contains all of the invited papers plus short manuscripts
expanding on the materials of the invited papers.
A total of about 85 participants came to the workshop. The
format of the conference was kept informal on purpose, so as to
facilitate the discussions. Unfortunately, these discussions, at
times intense, could not be included in this volume due to the lack
of secretarial help during the meeting.
A great deal of current information was exchanged during the
conference. However, the full impact of a conference can only be
realized when the proceedings have been published and read by par
ticipants as well as other colleagues in this field of physics who
were not in attendance. We sincerely hope that these proceedings
will be useful in this regard.
The Organizing Committee is particularly grateful to the
Conference participants for their patience and in helping us pre
pare the proceedings. The generous financial help of Drexel Uni
versity, University of Tennessee and Vanderbilt University was
instrumental in making this conference a reality, and is greatly
appreciated. Last but not least, the professional help of
Mr. Palliparambil Joseph Antony deserves to be especially mentioned,
without which completion of this volume would have been impossible.
The Editors
v
CONTENTS
Note: The name in capitals indicates the author
who presented the talk.
SESSION I: High Spin Phenomena
Chairperson: L.L. Riedinger
Quasi-Particle Motion in Rotating Nuclei 1
S. FRAUENDORF
Nuclear Spectroscopy at Very High and Very Low
Rotational Frequencies 29
J.D. GARRETT
Dynamic Deformation Theory: Recent Results for
Spectra and for Cross Sections 55
K. KUMAR
High Spin Phenomena 83
J.H. HAMILTON and C.F. Maguire
Interpretation of the 2l-ns Isomer in 109Hg as
(Vi13/2)2 from a g-Factor Measurement 103
S.A. HJORTH, I.Y. Lee, J.R. Beene, C. Roulet,
D.R. Haenni, N.R. Johnson, F.E. Obenshain
and G.R. Young
High Spin Studies by Multiple Coulomb Excitation 109
E. GROSSE
SESSION II: Heavy-Ions Reactions
Chairperson: R.K. Bhaduri
On the Transition from the Coherent to the Statistical
Phase in Deep Inelastic Collisions
121
U. SMILANSKY, S. Mukamel, D.H.E. Gross
and K. Mohring
vii
viii CONTENTS
Excitation of Shape-Vibrational Modes in Nuclei by
Relativistic Heavy Ions 141
J.O. RASMUSSEN, J. Blair and X. Qiu
Nuclear Charge and Matter Distributions 153
P . E. HODGSON
A Study of the Reaction Mechanism for l2C on 209Bi
at E(C) = 61.1-73 MeV 177
GEN-MING JIN, Xie Yuan-Xiang, Zhu~ong-Tai
Shen Wen-Qing, Yu Ju-Sheng, Sun Xi-Jun,
Liu Guo-Xing, Sun Ching-Chang, Gua Jun-Sheng,
Wu Zhon-Gli, Xu Shu-Wei, Wu En-Chin and
Yang Chen-Zhong and J.D. Garrett
SESSION III: Transfer Reactions
Chairperson: E. Grosse
Inelastic Scattering and Transfer Reactions Using
Very Heavy Ions 193
M.W. GUIDRY, R.E. Neese and T.L. Nichols
Probing Transitional Regions with Nuclear Transfer
223
Reactions
J. VAAGEN
249
Nuclean Reactions Near the Coulomb Barrier
J.S. Lilley
275
Heavy Ion Reaction Mechanisms
C.F. Maguire and J.H. HAMILTON
Heavy-Ion Induced Transfer Reactions to High-J
Orbital States 297
J. BARRETTE
SESSION IV: Microscopic Theories of Nuclear Structure
Chairperson: A. Klein
Perturbation Theory for a System of Fermions in a
Deformed Basis 309
D.R. BES
The Boson Fermion-Hybrid Representation and
The Nuclear Field Theory 317
C.L. WO, M.W. Guidry, J.Q. Chen and D.H. Feng
CONTENTS
Microscopic Calculations of the Fission Barrier of
Some Actinide Nuclei with Skyrme-Type Interaction
Using a Two-Step Iterative Method 331
A. Dutta, R.K. Bhaduri, I. Easson, M. Kohno
and M. Val1i~res
Linear_.Response RPA Model to Open Shell Nuclei 341
A. Moa1em and J. Bar-Touv
Collective Gyromagnetic Ratio From Density Dependent
Hartree-Fock Calculations 349
D.W.L. Sprung, S.G. Lie and M. Va11i~res
A Phenomenological Study of Nuclear Currents 357
C.L. Lin
Collective Vibrations with Zero Range Skyrme and
Delta-Log Interaction 363
A. Abbas
SESSION V: Interacting Boson Model
Chairperson: E. Marshalek
Overview of Experimental Tests of the IBA 369
R.F. CASTEN
The Interacting Boson Model in the Continuous
Basis Representation 4ll
R. GILMORE and D.H. Feng
Shell Model Structure of the Interacting Boson Model
and the Interacting Boson Fermion Model 435
I. TALMI
Testing the Interacting-Boson and Interacting-Boson
Fermion Approximations by the Study of Radioactive
4ll
Decay Schemes with UNISOR On-Line Isotope-Separator
J.L. WOOD
Studies of Isotope Series with Effective Boson
Hamiltonians 4~
P. FEDERMAN, O. Castanos and A. Frank
Use of a Boson Mapping to Elucidate the Relation
ship Between the IBM and the Bohr Collective
Hamiltonian and between a Simplified Shell Model
and the Bohr Collective Hamiltonian 487
A. Klein and M. Val1i~res
x CONTENTS
Renormalization of the IBA Hamiltonian for the
Effects of the g Boson 495
K.A. SAGE and B.R. Barrett
The Interacting-Boson-Fermion Approximation 503
O. SCHOLTEN
Quantized Bogolyubov Transformation and
Microscopic Foundation of IBM 523
LI-MING YANG
SESSION VI: Miscellaneous Topics
Chairperson: S. Pittel
Theory of Nuclear Single Particle Potential 531
SHI-SHU WU
Application of The Boson-Fermion Hybrid Representation:
Why is Spin-Polarized Atomic Hydrogen a Bosonic System? 563
C.L. Wu, J.M. Yuan and D.H. Feng
The Microscopic Mechanism of the (p, ~t) Reaction 5n
Liu Bo and Zhang Zong-Ye
Supermultiplet Classification and Collective Spectra
of Two-Electron Atoms
5~
Michael E. KELLMAN
PARTICIPANTS 5~
INDEX 591
QUASIPARTICLE MOTION IN ROTATING NUCLEI
S. Frauendorf
Central Institute for Nuclear Research
Rossendorf, 8051 Dresden, PF 19
German Democratic Republic
1. ABSTRACT
The rotational bands of deformed nuclei with high spin can be
interpreted as configurations of independent quasipartic1es in a
deformed potential rotating with a constant frequency and with a
pairfie1d present. This generalization of the shell model to rotat
ing potentials is called the Cranked Shell Model (CSM). The classi
fication with respect to the symmetry quantum number signature is
introduced. Several CSM-predictions, such as the additivity of
quasiparticle energies and angular momenta, the occurrence of char
acteristic frequencies around which band crossings cluster and the
interference between quasiparticle orbits are discussed and compared
with experimental data on high spin states in the light rare earth
region.
II. INTRODUCTION
The ascent of heavy ion accelerators has created the possibility
to study nuclei that carry as much angular momentum as they can
accomodate without fissioning. The region of a few MeV excitation
above the yrast line is being intensively studied. In this yrast
region the rotating nucleus is cold, i.e. its level density is com
parable with that near the ground state. Moreover, it takes the
rotating nucleus at least 10-12s to de-excite into the ground state.
This time is very long in comparison with the typical nuclear time
of 10-22s and the states in the yrast region may be considered as
stationary ones. This led to the concept of "Yrast-spectroscopy"
which extends the spectroscopy of low lying states to the whole
yrast region1 . Recent experimental yrast-spectroscopy of discrete
2 s. FRAUENDORF
Y-lines has reached angular momentum of I ~ 30 t 2• The region of
higher angular momenta is being explored by studying the Y-continua3
Since the nucleus is cold in the yrast region the mean free
path of the nucleons is large enough that the independent particle
model is expected to work. The majority of the excited states above
the yrast line should correspond to a rearrangement of a few nucle~
onic orbitals. Thus it is obvious to base the analysis of the yrast
region on an appropriate version of the shell model. One may dis
tinguish two important cases:
i. The nucleus rotates about its symmetry axis. The rotation
does not directly modify the nucleonic orbits (only via changes of
the potential) and one may employ the standard shell model with a
spherical or deformed potential. The experimental data are con
sistent with such an approachl ,4.
ii. The nucleus rotates about an axis perpendicular to its symmetry
axis. The rotation of the deformed potential modifies the nucleonic
orbits which depend on the angular frequency. The rotation is col
lective and the states group into rotational bands.
My talk will only deal with case (ii). It is based mainly on
the work by R. Bengtsson and S. Frauendorf5,6 (cf. also ref. 1).
III. THE CRANKED SHELL MODEL
We assume that the deformed shell-model potential rotates with
the constant angular frequency w about an axis perpendicular to
its symmetry axis. In the frame of reference attached to the poten
tial the shell model Hamiltonian reads
h' h - wjx (1)
where h is a standard deformed shell model Hamiltonian and z and
x are chosen to be the symmetry and rotation axis, respectively.
We suggest calling the Hamiltonian the "Cranked Shell Model" (CSM)
in order to relate it to the Cranking Model. The latter notation
(also Cranking HFB) is usually used in the context of a self
consistent treatment of the independent particle Hamiltonian (1),
providing total excitation energies with respect to the ground
state. The simpler CSM continues the tradition of shell models
assuming that h does not depend on the configuration; h may depend
on w, but so far the consequences of this possibility have not been
studied in a detail. As any shell model, CSM aims only at the cal
culation of excitation energies with respect to a reference con
figuration that depends on the frequency w (a band which is yrast
of near yrast~.
